## NCERT Solution for Class 8 Maths-Rational Numbers

** Class 8 Maths – Rational Numbers : **In mathematics, we usually come across different terms like natural number, whole numbers, integers and rational number. We will discuss rational number in this article from

**8th**

^{ }Class Maths.

Let’s us revisit the properties of Rational numbers in **class 8.**

__Rational Numbers__

A rational number is a number that can be written in the form of P/Q where P and Q are integers and Q is not equal to 0.

Example:-5/7, (-2/3)

__Properties of Rational numbers__

We will first discuss the properties of rational numbers.

__Closure Property__

We call a set of numbers closed under operation if performance of that operation on members of the set of numbers always creates a member of the same set only; in this case we also say that the set is closed under the operation.

__Under addition__

Rational numbers are closed under addition.For any two rational numbers a and b,a+b is also a rational number.

__Under subtraction__

Rational numbers are closed under addition.For any two rational numbersaand b, a-b is also a rational number.

__Under Multiplication__

Rational statistics are closed under multiplication.For any two rational numbers a and b, a*b is also a rational number.

__Under Division__

Rational numbers are not closed under multiplication.For any rational number a, a/0 is not defined.

__Commutative Property__

As per commutative property, the interchanging order of numbers will not change the result.

__Under addition__

Two rational numbers can be added in any order.Addition is commutative for rational numbers.For any two rational numbers a and b, a+b=b+a

__Under subtraction__

Subtraction is not commutative for rational numbers.

__Under Multiplication__

Multiplication is commutative for rational numbers. For any two rational numbers a and b, a*b=b*a

__Under Division__

Division is not commutative for rational numbers

__Associative Property__

__Under addition__

Addition is associative for rational numbers.For any 3 rational numbers a,b, and c.

a + (b+c) = (a+b) +c

__Under subtraction__

Subtraction is not associative for rational numbers

__Under Multiplication__

Multiplication is associative for rational numbers.For any 3 rational numbers a,b, and c.

a *(b * c) = (a * b) *c

__Under Division__

Division is not associative for rational numbers.

*For illustrations and solved NCERT solutions, visit Class 8 NCERT Maths solutions*

__The Role of Zero__

Zero is called the identity for the addition of rational numbers.It is the additive identity for integers and whole numbers as well.

a+0=0+a=a

b+0=0+b=b

__The role of 1__

1 is the multiplicative identity of rational numbers.

a*1=1*a=a

__Negative of a number__

For any rational number a/b, we have a/b+(-a/b)=(-a/b)+a/b=0.We say that (-a/b) is the additive inverse of a/b and a/b is the additive inverse of (-a/b).

__Reciprocal__

A rational number c/d is called the reciprocal or multiplicative inverse of another rational number a/b, if a/b*c/d=1.

__Distributive property of multiplication over addition and subtraction__

For all rational numbers a,b, and c

a (b+c)=ab+ ac

a(b-c)=ab-ac

__Rational Numbers between two rational numbers__

Let’s consider the below example for **8th class maths**

Q – Find rational number -1/10 and 3/10?

Sol- Rational numbers -1/10 and 3/10 are

0/10,1/10/2/10

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